Best emo songs by non-emo bands?
My #1 pick (and definitely in my top 8 emo songs canon) would be "Breakaway Terminal Cable" by Cerberus Shoal, who had a rather odd band trajectory, going from emo-esque post-rock to post-rock/experimental folk. Also, if you know who Big Blood are, you'd probably know (or like to know) that they formed from the ashes of Cerberus Shoal. I also really love "JBO vs. Blin", off Cerberus Shoal's second album.
"Nar det blaser pa manen" by Kent. I'm guessing they're kinda like Muse or Coldplay if they were Swedish and also much better. Definitely a great MWE esque song, though. Speaking of Muse... "Sunburn" and "Muscle Museum" remind me of some early 00s alternative-prog-emo stuff like Coheed or Dear Hunter. Good songs, although "best" is a stretch.
"Cow" by Sparklehorse which is maybe debatably MWE but deserves a mention because it's one of the best songs ever and you should listen to it NOW. And LATER. Then do it again.
YMMV/Bonus: "Washer" by Slint. I consider Slint emo or at least adjacent, but I know many people don't. Regardless, "Washer" is definitely an emo song and an amazing one to boot.